Question

You wish to test the following claim (HaHa) at a significance level of α=0.01

      Ho:p=0.89
      Ha:p<0.89

You obtain a sample of size n=526 in which there are 461 successful observations.

Determine the test statistic formula for this test.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.89.
• There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.89.
• The sample data support the claim that the population proportion is less than 0.89.
• There is not sufficient sample evidence to support the claim that the population proportion is less than 0.89.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.89

Ha : p < 0.89

n = 526

= x / n =  461 / 526 = 0.88

P0 = 0.89

1 - P0 = 1 - 0.89 = 0.11

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.88 -0.89 / [0.89*0.11 / 526]

= −0.995

Test statistic = z = −0.99

P-value = 0.1599

= 0.01

P-value <

0.1599 ≥ 0.01

fail to reject the null

There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.89.